Arithmetic and Logic Unit

Computer Organization & Embedded System — Control and Central Processing Units, NEC licence examination syllabus (Nepal Engineering Council).

The Arithmetic and Logic Unit (ALU)

Where the actual computing happens.

The ALU is the CPU's calculator — a combinational circuit that takes two operand inputs and a function-select code, and produces a result. Depending on the select code, it can perform addition, subtraction, AND, OR, XOR, shifts, and comparisons.

Every ALU operation also updates a small set of status/condition flags — and these flags are what make decision-making in software possible. Every "if" statement you've ever written ultimately depends on one of these four flags being checked.

🚩 The Four Flags

Z (Zero)Set when the result is exactly zero.

C (Carry)Set when an addition overflows the register width, or a subtraction borrows.

S (Sign)Mirrors the most significant bit — tells you if the result is negative in two's complement.

V (Overflow)Set when a SIGNED arithmetic operation produces a result too large to represent correctly.

💡 Numerical trap to watch for: Carry flag and Overflow flag are NOT the same thing. Carry cares about unsigned overflow; Overflow (V) cares about signed overflow. Examiners love testing this distinction with a tricky addition example.

How a comparison actually works

The chapter says every if-statement depends on the flags. The mechanism is worth spelling out, because it explains why comparison and subtraction are the same operation.

CMP A, B compute A − B, set the flags, DISCARD the result JZ label jump if the Zero flag is set → A was equal to B JC label jump if Carry/Borrow was set → A was less than B A CMP is a subtraction whose answer nobody wants. Only the side effects on the flags are kept.

🚩 What each flag records

Zero (Z)The result was zero — so in a comparison, the two values were equal.

Carry (C)A carry out of, or borrow into, the most significant bit. For unsigned values this is the less-than test.

Sign (S/N)The most significant bit of the result — negative in two's complement.

Overflow (V)The signed result did not fit. This is the signed counterpart of carry.

Carry and overflow are constantly confused, and the distinction is exactly signed versus unsigned. Adding two 8-bit values, 200 + 100 sets carry because 300 exceeds 255 as an unsigned byte. Adding 100 + 100 as signed bytes sets overflow, because 200 exceeds the +127 signed limit and the result appears negative. The hardware sets both flags on every operation and the program chooses which to believe, according to how it is interpreting the bits.

💡 That is why processors have two sets of conditional branches — one family for unsigned comparisons reading carry, another for signed comparisons reading sign and overflow together. Using the unsigned branch on signed data is a real and hard-to-spot bug, and a good exam answer to "why does the ALU need both flags?"

Why the ALU is combinational

The ALU has no memory — outputs depend only on the current inputs, with no clock and no state. All the storage sits in the registers around it.

That is what allows a single ALU to be shared across every instruction: it computes continuously, and the control unit decides which function code to apply and where to route the result. The flags register is the one piece of state, and it exists precisely so a later instruction can act on what an earlier one computed.

Syllabus points

ALU functional block
Status/condition flags (Z, C, S, V)

Create a free account to tick topics off, take notes as you read, watch the video lessons and get a day-by-day study plan built around your exam date.